The invention described herein was made in the performance of work under a NASA Contract and is subject to the provisions of Section 305 of the National Aeronautics and Space Act of 1958, as amended, Public Law 85-568 (72 Stat. 435; 42 USC 2457).
1. Field of the Invention
The present invention relates generally to steady state and transient flow in a complex fluid network. It relates in particular to a program implemented on a computer for analyzing steady state and transient flow in a complex fluid network to provide modeling of phase changes, compressibility, mixture thermodynamics, and external body forces.
2. Description of Related Art
A fluid flow network consists of a group of flow branches, such as pipes and ducts, that are joined together at a number of nodes. They can range from simple systems consisting of a few nodes and branches to very complex networks containing many flow branches, simulating valves, orifices, bends, pumps and turbines. In the analysis of existing or proposed networks, some node pressures and temperatures are specified or known. The problem is usually to determine all unknown nodal pressures, temperatures and branch flow rates.
An accurate prediction of axial thrust in a liquid rocket engine turbopump requires the modeling of fluid flow in a very complex network. Such a network involves the flow of cryogenic fluid through extremely narrow passages, flow between rotating and stationary surfaces, phase changes, mixing of fluids and heat transfer. Propellant feed system designers are often required to analyze pressurization or blow down processes in flow circuits consisting of many series and parallel flow branches containing various pipe fittings and valves using cryogenic fluids.
Available commercial systems including computer codes are generally suitable for steady-state, single phase incompressible flow. Because of the confidential proprietary nature of such codes, it is not possible to extend their capability to satisfy the above mentioned needs. In the past, specific purpose codes were developed to model the Space Shuttle Main Engine (SSME) turbopump. However, it was difficult to use those codes for a new design without making extensive changes in the original code. Such efforts often turned out to be time consuming and inefficient. Therefore, the present Generalized Fluid System Simulation Program (GFSSP) has been developed as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces, such as gravity and centrifugal effects, in a complex flow network.
The oldest method for systematically solving a problem consisting of steady flow in a pipe network is the Hardy Cross method. Hardy Cross, xe2x80x9cAnalysis of Flow in Networks of Conduits or Conductorsxe2x80x9d, Univ. Ill., Bull. 286, November, 1936. Not only is this method suited for solutions generated by hand, but it has also been widely employed for use in computer generated solutions. But as computers allowed much larger networks to be analyzed, it became apparent that the convergence of the Hardy Cross method might be very slow or even fail to provide a solution in some cases. The main reason for this numerical difficulty is that the Hardy Cross method does not solve the system of equations simultaneously. It considers a portion of the flow network to determine the continuity and momentum errors. The head loss and the flow rates are corrected, and then it proceeds to an adjacent portion of the circuit. This process is continued until the whole circuit is completed. This sequence of operations is repeated until the continuity and momentum errors are minimized. It is evident that the Hardy Cross method belongs in the category of successive substitution methods, and it is therefore likely that it may encounter convergence difficulties for large circuits. In later years, the Newton-Raphson method has been utilized to solve large networks, and with improvements in algorithms based on the Newton-Raphson method, computer storage requirements are not much larger than those needed by the Hardy Cross method. See Jeppson, Ronald W., xe2x80x9cAnalysis of Flow in Pipe Networksxe2x80x9d, Ann Arbor Science, 1977.
The flow of fluid in a rocket engine turbopump can be classified into two main categories. The flow through the impeller and turbine blade passages is designated as primary flow. Controlled leakage flow through bearings and seals for the purpose of axial thrust balance, bearing cooling and rotodynamic stability is referred to as secondary flow. Flows in the blade passages are modeled by solving Naiver-Stokes equations of mass, momentum and energy conservation in three dimensions. Naiver-Stokes methods, however, are not particularly suitable for modeling flow distribution in a complex network.
Most of the available commercial software packages for solving flow networks are based on either the successive substitution method or on the Newton-Raphson method, and they are only applicable for a single phase incompressible fluid. Crane Company, xe2x80x9cFlow of Fluids Through Valves, Fittings and Pipexe2x80x9d, Technical Paper No. 410, 1969; Kelix Software System, xe2x80x9cProtopipe for Windows, Version 1.0, 1993-95. These are not suitable for modeling rocket engine turbopumps where mixing, phase change and rotational effects are present. Public domain computer programs have been developed in the aerospace industry to analyze the secondary flow in the SSME turbopumps. These programs use real gas properties to compute variable density in the flow passage. Mixing of fluids, phase changes and rotational effects, however, are not considered by these programs. See, e.g., Anderson, P. G., et al., xe2x80x9cFluid Flow Analysis of the SSME High Pressure Oxidizer Turbopumpxe2x80x9d, Lockheed Report No. LMSC-HREC TR D698083, August 1980.
It is therefor a primary object of the present invention to provide what has been heretofore unavailable in the prior art, viz., a robust and efficient computer implemented program to solve a system of equations describing a flow network containing phase changes, mixing and rotation, thereby affording practical modeling of phase changes, compressibility, mixture thermodynamics and external body forcesxe2x80x94all of which are objective results, highly useful and very much sought after by the design engineer.
The present invention is basically a general purpose computer program for analyzing steady state and transient flow in a complex network, the program being capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program""s preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches.
The present invention contains subroutines for computing xe2x80x9creal fluidxe2x80x9d thermodynamic and thermophysical properties for 12 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, water, and kerosene (RP-1). The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas.
A number of different resistance/source options are applicable for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thomson device.
The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This invention is also applied and verified through demonstrated examples.
Earlier programs that were used to analyze flow in SSME turbomachinery used a very simplified form of the momentum equation, only considering pressure and frictional forces. A more generalized form of the momentum equation is necessary to account for rotational effects. The momentum equation used in GFSSP includes inertia, pressure, friction, gravity, centrifugal and any external momentum sources. The frictional effects are proportional to the square of mass flow rate in the branch. The proportionality constant was derived from empirical information available in the literature.
The thermodynamic and thermophysical properties required in the conservation equations are obtained from two thermodynamic property programs, GASP and WASP, Hendricks, R. C., Baron, A. K., and Peller, I. C., xe2x80x9cA computer code for calculating the thermodynamic and transport properties for ten fluids: Parahydrogen, helium, neon, methane, nitrogen, carbon monoxide, oxygen, fluorine, argon, and carbon dioxidexe2x80x9d, NASA TN D-7808, February, 1975; Hendricks, R. C., Peller, I. C., and Baron, A. K., xe2x80x9cWASPxe2x80x94A flexible Fortran IV computer code for calculating water and steam propertiesxe2x80x9d, NASA TN D-7391, November, 1973. GASP and WASP provide thermodynamic and thermophysical properties for helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, and water. The properties of RP-1 fuel have been provided as a look up table. A real gas formulation has been used to compute mixture properties. The invention also includes the options of modeling any incompressible fluid of constant density and viscosity or an ideal gas.
The invention includes a preprocessor to facilitate the creation of the model. With the help of this preprocessor, a user without a substantial background in computational methods or the FORTRAN programming language can model complex flow circuits.
The task of the computational model is to obtain a simultaneous solution of the governing equations. This system of equations is solved by GFSSP utilizing a novel numerical procedure which is a combination of Newton-Raphson and successive substitution methods.
The capability to model transient flow is included in the present invention. The transient capability allows the user to model pressurization and blow down processes. GFSSP""s transient predictions have been verified by comparing the predictions with the analytical solutions. The user is also provided with the capability to model a heat exchanger and a turbopump. An additional resistance option is provided to model the Joule-Thomson effect that occurs in a viscojet.